Problem: Simplify the following expression: $z = \dfrac{a^2 - 8a - 9}{a - 9} $
First factor the polynomial in the numerator. $ a^2 - 8a - 9 = (a - 9)(a + 1) $ So we can rewrite the expression as: $z = \dfrac{(a - 9)(a + 1)}{a - 9} $ We can divide the numerator and denominator by $(a - 9)$ on condition that $a \neq 9$ Therefore $z = a + 1; a \neq 9$